Combine balsamic vinegar, 4 teaspoons garlic, rosemary, salt and pepper in bowl. Add olive oil in a slow stream while constantly whisking until well combined.
Prepare Grilled & Ready Chicken Breast Strips in skillet according to package directions. Reserve 4 tablespoons balsamic dressing for greens and add rest to skillet with chicken and warm through.
Combine greens, tomatoes and onions and toss with reserved 4 tablespoons of balsamic dressing.
In bowl whisk mayonnaise, Dijon mustard, 2 teaspoons garlic, salt and pepper.
To assemble: place rolls on flat work surface and cut in half. Spread mayonnaise mixture on top and bottom of each bun. Divide meat among buns, top with greens and close top of bun.
For the salad, place greens in bowl, add chicken, onions, tomatoes and balsamic dressing.